Question: Simplify the following expression and state the condition under which the simplification is valid. $z = \dfrac{5x^2 + 10x - 40}{4x^2 - 20x + 24}$
First factor out the greatest common factors in the numerator and in the denominator. $ z = \dfrac {5(x^2 + 2x - 8)} {4(x^2 - 5x + 6)} $ $ z = \dfrac{5}{4} \cdot \dfrac{x^2 + 2x - 8}{x^2 - 5x + 6} $ Next factor the numerator and denominator. $ z = \dfrac{5}{4} \cdot \dfrac{(x - 2)(x + 4)}{(x - 2)(x - 3)}$ Assuming $x \neq 2$ , we can cancel the $x - 2$ $ z = \dfrac{5}{4} \cdot \dfrac{x + 4}{x - 3}$ Therefore: $ z = \dfrac{ 5(x + 4)}{ 4(x - 3)}$, $x \neq 2$